Semantic Substrate Dynamics Theory: An Operator-Theoretic Framework for Geometric Semantic Drift

Semantic Substrate Dynamics Theory (SSDT) proposes an operator‑theoretic framework that unifies various signals of semantic drift—such as embedding displacement, neighbor change, distributional divergence, and recursive trajectory instability—by treating them as observables of a time‑indexed substrate that couples embedding geometry to a local diffusion kernel. The theory distinguishes between within‑basin churn, basin crossing, recursion‑induced instability, and intervention‑order effects, using coarse Ricci curvature as a dense descriptor of basin and bridge geometry and bridge mass as a sparse node‑level indicator of genuine bridge structure. For recursive generation, SSDT decomposes node displacement into radial and tangential components, separating bounded departure from ongoing reinterpretation, and predicts future rewiring through a local density statistic rather than curvature aggregates.

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• rag
• diffusion